Optimal. Leaf size=25 \[ -x+\frac {5}{\log \left (1-x \left (e^{2209}+e^{1+x} x\right )\right )} \]
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Rubi [A] time = 0.41, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 3, number of rules used = 2, integrand size = 101, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6688, 6686} \begin {gather*} \frac {5}{\log \left (-e^{x+1} x^2-e^{2209} x+1\right )}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {5 e \left (e^{2208}+e^x x (2+x)\right )}{\left (-1+e^{2209} x+e^{1+x} x^2\right ) \log ^2\left (1-e^{2209} x-e^{1+x} x^2\right )}\right ) \, dx\\ &=-x-(5 e) \int \frac {e^{2208}+e^x x (2+x)}{\left (-1+e^{2209} x+e^{1+x} x^2\right ) \log ^2\left (1-e^{2209} x-e^{1+x} x^2\right )} \, dx\\ &=-x+\frac {5}{\log \left (1-e^{2209} x-e^{1+x} x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 27, normalized size = 1.08 \begin {gather*} -x+\frac {5}{\log \left (1-e^{2209} x-e^{1+x} x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 42, normalized size = 1.68 \begin {gather*} -\frac {x \log \left (-x^{2} e^{\left (x + 1\right )} - x e^{2209} + 1\right ) - 5}{\log \left (-x^{2} e^{\left (x + 1\right )} - x e^{2209} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 26, normalized size = 1.04
method | result | size |
risch | \(-x +\frac {5}{\ln \left (-x^{2} {\mathrm e}^{x +1}-x \,{\mathrm e}^{2209}+1\right )}\) | \(26\) |
norman | \(\frac {5-x \ln \left (-x^{2} {\mathrm e} \,{\mathrm e}^{x}-x \,{\mathrm e}^{2209}+1\right )}{\ln \left (-x^{2} {\mathrm e} \,{\mathrm e}^{x}-x \,{\mathrm e}^{2209}+1\right )}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 42, normalized size = 1.68 \begin {gather*} -\frac {x \log \left (-x^{2} e^{\left (x + 1\right )} - x e^{2209} + 1\right ) - 5}{\log \left (-x^{2} e^{\left (x + 1\right )} - x e^{2209} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 13.04, size = 25, normalized size = 1.00 \begin {gather*} \frac {5}{\ln \left (1-x^2\,\mathrm {e}\,{\mathrm {e}}^x-x\,{\mathrm {e}}^{2209}\right )}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 20, normalized size = 0.80 \begin {gather*} - x + \frac {5}{\log {\left (- e x^{2} e^{x} - x e^{2209} + 1 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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